Parametrizing Convex Sets Using Sublinear Neural Networks

• URL: http://arxiv.org/abs/2605.03520v1
• Date: Tue, 05 May 2026 08:57:38 GMT
• Title: Parametrizing Convex Sets Using Sublinear Neural Networks
• Abstract summary: We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions.<n>Our networks implicitly represent both the support and gauge functions of a convex body.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal approximation theorem for convex sets under this parametrization. Empirically, we demonstrate the method on shape optimization and inverse design tasks, achieving accurate reconstruction of target shapes.

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